For me, the OP raises two points, one trivial the other interesting.

The late check out time limit appears undefined, unspecified. Presumably this is part of the availability question and subject to some negotiation.


The term "available" is ambiguous. We run into this ambiguity where guests are refused availability dependent upgrades, when the target upgrade is seen to be available (for cash) on the website: clearly in this upgrade case there is an element opportunity cost analysis - the hotel expects to be able to sell the room so refuses to release it as available for upgrade.

For late check-out the situation is less clear - seems to be either the room is needed before 14:00 (or 15:00 or 16:00) or it isn't. To take cash to make it available creates the impression the reservation team is willing to risk inconveniencing an incoming guest in return for a quick buck.